A216071 Brocard's problem: positive integers m such that m^2 = n! + 1 for some n.

5, 11, 71

Offset: 1

Author

V. Raman, Sep 01 2012

Keywords

• nonn
• hard
• bref

Comments

See A085692 and A146968 for links, references and comments. - M. F. Hasler, Nov 20 2018

Links

• Wikipedia, Brocard's problem

Crossrefs

A085692, A146968, A216071 are all essentially the same sequence. - N. J. A. Sloane, Sep 01 2012

Programs

Mathematica

Sqrt[#!+1]&/@Select[Range[1000],IntegerQ[Sqrt[#!+1]]&] (* Harvey P. Dale, Sep 29 2012 *)

PARI

apply( sqrtint, A085692) \\ M. F. Hasler, Nov 20 2018

PARI

select( is_A216071(m)=m^2==A084558(m^2)!+1, [0..99]) \\ M. F. Hasler, Nov 20 2018

Formula

a(n) = A000196(A085692(n)) = A000196(A038507(A146968(n))) where A000196 = sqrt and A038507(n) = n! + 1. - M. F. Hasler, Nov 20 2018